Orbits in Symmetric Spaces and Isomorphic Lattices with Applications to Orlicz – Lorentz Spaces

Abstract

We study the general extreme points of convex fully symmetric sets of measurable linear operators. Weak convergence and isometries of non-commutative symmetric and Lorentz spaces are considered. We also show the duality of Orlicz-Lorentz space and give the determination of minimal projection and extensions in Lebesgue measure on the real line with two-dimensional and symmetric spaces with maximal projection constants. We show the characterization of singular symmetric functional and the behaviour of sequences of orbits in symmetric spaces. We establish the isomorphic measurable functions of the Lebesgue subspaces and copies in the lattice and its symmetrization with applications to Orlicz-Lorentz space. Chalmers-Metcalf operator and uniqueness of minimal projections with two presented examples of spaces and with maximal projection constant are considered. We extend the three-dimensional subspace of essential Hilbert space of five - dimensional with maximal projection constant.